Theoretical Investigation on Nonlinear Multimode Interference Couplers Based on Volterra Series

In this paper, a theory to characterize nonlinear Kerr effect in multimode interference (MMI) couplers is presented. The theory is based on the solution for the spatial nonlinear Schrödinger equation (SNLSE) with the Volterra series. The derivation is first conducted for the 1-D MMI couplers and later extended to the 2-D MMI couplers. It is revealed in the analysis that the first order component of the Volterra series is actually the exact solution for the SNLSE when the nonlinear effect is negligible. Numerical simulation shows the third order component of the Volterra series provides an accurate prediction for the nonlinear evolution inside MMI couplers. The derived analytical formulas can provide a deep insight into the nonlinear effects in MMI couplers and other planar multimode waveguides.